Study GuidesExam QuestionsPast Papers
AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 7: OscillationsEnergy of Simple Harmonic Oscillators

Energy of Simple Harmonic Oscillators (College Board AP® Physics 1: Algebra-Based): Exam Questions

15 mins15 questions

Select a download format for Energy of Simple Harmonic Oscillators

Scroll for more
Easy
Medium
Hard
1
Sme Calculator1 mark

The total energy E of a system in simple harmonic motion reflects the energy transfers between the kinetic energy K store and the potential energy U store.

Which of the following is the correct equation for the total energy of a system in simple harmonic motion?

  • E space equals space U space minus space K

  • E space equals space U space cross times space K

  • E space equals space K over U

  • U space equals space E space minus space K

Choose your answer

Did this page help you?

2
Sme Calculator1 mark

A pendulum on Earth, consisting of a mass on a string, oscillates in simple harmonic motion.

Which of the following statements is true about the energy of the pendulum-Earth system?

  • The total kinetic energy of the pendulum-Earth system is constant.

  • The total energy of the pendulum-Earth system is constant.

  • The total gravitational potential energy of the pendulum-Earth system is constant.

  • All of the above

Choose your answer

Did this page help you?

3
Sme Calculator1 mark

Which of the following correctly describes the relationship between potential and kinetic energy in a simple harmonic oscillator?

  • The sum of kinetic and potential energies remains constant throughout the motion.

  • The kinetic energy is maximum when the potential energy is maximum.

  • The potential energy increases as the object passes through the equilibrium position.

  • The total energy of the system varies depending on the position of the object.

Choose your answer

Did this page help you?

4
Sme Calculator1 mark

An ideal horizontal mass-spring system undergoes simple harmonic motion.

Which of the following quantities does the total energy of the system depend on?

  • The spring constant and the amplitude of oscillation.

  • The mass of the object and gravitational field strength.

  • The spring constant and the mass of the object.

  • The unstretched length of the spring and the amplitude of oscillation.

Choose your answer

Did this page help you?

5
Sme Calculator1 mark

A mass-spring system undergoes simple harmonic oscillations over a horizontal frictionless surface.

If a small frictional force is applied to the system, which of the following correctly describes the change to the amplitude of the oscillations over time?

  • The amplitude increases.

  • The amplitude decreases.

  • The amplitude remains constant.

  • There is not enough information to determine the effect on the amplitude.

Choose your answer

Did this page help you?

1
Sme Calculator1 mark

A mass is attached to a vertical spring and allowed to reach equilibrium. It is then displaced by a distance d and released. The total energy and time period are E subscript t o t end subscript and T respectively. In a second investigation, the same mass-spring system oscillates but travels twice as fast through equilibrium.

Which line correctly identifies the total energy and time period of the new oscillations, E subscript t o t comma n e w end subscript and T respectively?

E subscript t o t comma n e w end subscript

T subscript n e w end subscript

A

2 E subscript t o t end subscript

T over 2

B

4 E subscript t o t end subscript

T over 2

C

2 E subscript t o t end subscript

2 T

D

4 E subscript t o t end subscript

T

Choose your answer

Did this page help you?

2
Sme Calculator1 mark
Two systems each feature a horizontal spring attached to a wall. In both systems, a block of mass m is attached to the free end of the spring. The first system has a spring constant k. The second system has a spring constant 4k. Both blocks are at equilibrium (x = 0) travelling rightwards with the same speed v_max.

Two object-spring systems oscillate on horizontal, frictionless surfaces, as shown in the figure. The first system oscillates with amplitude A.

Which of the following expressions correctly represents the amplitude of the second system?

  • A over 2

  • A

  • 2 A

  • 4 A

Choose your answer

Did this page help you?

3
Sme Calculator1 mark

A mass-spring system oscillates on a horizontal frictionless surface. Which of the following is proportional to the system's total energy?

  • The square of both the mass and the amplitude

  • Mass and displacement of the object

  • Angular frequency

  • Mass and the square of the amplitude

Choose your answer

Did this page help you?

4
Sme Calculator1 mark

A mass is attached to a vertical spring and allowed to extend until the mass-spring system comes to rest. It is then extended further and released. The total energy and time period of the oscillations are E subscript T and T respectively. In a second investigation, the same mass-spring system travels twice as fast at equilibrium.

Which of the following correctly describes the total energy and time period of the oscillations in the second investigation?

 

Total Energy

Time Period

A.

2 E subscript T

T over 2

B.

4 E subscript T

T over 2

C.

2 E subscript T

2 T

D.

4 E subscript T

T

    Choose your answer

    Did this page help you?

    1
    Sme Calculator    1 mark

    An ion in a crystal lattice structure oscillates with simple harmonic motion. The period of the oscillation is T which is measured from equilibrium.

    Which of the following graphs shows the change in kinetic energy of the ion from time t = 0 to t = T over 2?

    Four graphs labeled A, B, C, and D display different waveforms with time (t) on the x-axis and energy (E) on the y-axis. Graph A: E increases from 0 to a maximum, returns to zero, drops to a negative minimum and then returns to 0 at a time of T/2. Graph B: E starts at a maximum, drops to zero and returns to a maximum at time T/2 Graph C: E starts at a maximum, drops to zero, returns to the maximum a second time, drops to zero and finishes at a third maximum at time T/2 Graph D: E starts at zero, increases to a maximum and then decreases to zero again by time T/2

    Choose your answer

    Did this page help you?

    2
    Sme Calculator    1 mark

    A block-spring system oscillates horizontally with an amplitude of 8 m.

    When the displacement of the block from equilibrium is 5 m, which of the following is most nearly the ratio of the kinetic energy to potential energy of the system?

    • 0.4

    • 0.6

    • 1.6

    • 2.6

    Choose your answer

    Did this page help you?

    3
    Sme Calculator    1 mark
    An energy bar chart is shown with three bars. The first bar, labelled U_s is three quarters the height of the axis. The second bar, labelled K, is one quarter of the height of the y axis. The third bar, labelled U_G, has a height of zero.

    An object-spring-Earth system oscillates vertically in simple harmonic motion. The energy bar chart in the figure shows the elastic potential energy U subscript s, kinetic energy K, and gravitational potential energy U subscript G of the object at the equilibrium position.

    Which of the following most closely represents the energy bar chart of the system when the object is at the lowest point of the oscillation?

    Graph A: U_s is nearly the full height of the positive axis, K has zero height and U_G is small and positive. Graph B: U_s is zero, K is the full height of the positive axis and U_G is half the height of the positive axis. Graph C: U_s is taller than the positive axis, K is zero and U_G is negative and a quarter of the height of the negative axis Graph D: U_s is three quarters the height of the positive axis, K is zero and U_G is negative and three quarters the height of the negative axis

      Choose your answer

      Did this page help you?

      4
      Sme Calculator      1 mark
      A graph of energy against time. One line, labelled E_K, has an initial energy value of zero and increases linearly to 2.0 J over 5 s. The other line, labelled E_P, has an initial energy value of 8.0 and decreases linearly to 7.0 J over 5 s.

      The graph shows the variation in kinetic and potential energies of an oscillating system.

      Which of the following statements is true?

      • The system does work on the surroundings.

      • The surroundings do work on the system.

      • No work is done on or by the system.

      • It cannot be determined whether the system or the surroundings do work.

      Choose your answer

      Did this page help you?

      5
      Sme Calculator      1 mark

      A mass attached to a spring oscillates in SHM with amplitude A.

      Which of the following expressions describes the displacement of the mass from the equilibrium position when the kinetic energy and potential energy of the system are equal?

      • 0

      • plus-or-minus A over 2

      • plus-or-minus fraction numerator A over denominator square root of 2 end fraction

      • plus-or-minus A

      Choose your answer

      Did this page help you?

      6
      Sme Calculator      1 mark

      An unloaded spring initially hangs vertically. A mass m is added to the spring and allowed to extend by a length d where it hangs at rest. The mass is then displaced by distance A and released, where A space less than space d. The system then undergoes simple harmonic oscillations.

      Taking gravitational potential energy as zero at the lowest point, which of the following expressions represents the potential energy of the Earth-spring-mass system at the highest point?

      • 1 half k A squared space plus space 2 m g A space

      • 1 half k open parentheses d minus A close parentheses squared space plus space m g A

      • 1 half k open parentheses d plus A close parentheses squared space plus space m g A

      • 1 half k open parentheses d minus A close parentheses squared space plus space 2 m g A

      Choose your answer

      Did this page help you?